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- Pedro Real
- 1999

We present here a combinatorial method for computing Steenrod squares of a simplicial set X. This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face… (More)

We present a new solution for the Homology Groups of Binary 2D Image (HGB2I) Problem by using Membrane Computing techniques. This is a classical problem in Homology Theory which tries to calculate the number of connected components and the representative curves of the holes of these components from a given binary 2D image. To this aim, we present a family… (More)

In this paper, working over Z (p) and using algebra perturbation results from [18], p-minimal homological models of twisted tensor products (TTPs) of Car-tan's elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological model of a inde-composable p-minimal TTP of length (≥ 2) of exterior… (More)

Once a discrete Morse function has been defined on a finite cell complex, information about its homology can be deduced from its critical elements. The main objective of this paper is to define optimal discrete gradient vector fields on general finite cell complexes, where optimality entails having the least number of critical elements. Our approach is to… (More)

- R González, Díaz, P Real
- 2002

Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes ([Mun84], [DE95,ELZ00], [DG98]), but concerning the algorithmic treatment of cohomology operations, very little is… (More)

- Jean-Luc Mari, Pedro Real
- 2007

In this paper, we introduce a simple and original algorithm to compute a three-dimensional simplicial complex topologically equivalent to a 3D digital object V , according to the 26-adjacency. The use of this adjacency generates issues like auto-intersecting triangles that unnecessarily increase the dimensionality of the associated simplicial complex. To… (More)

- Daniel Dı́az-Pernil, Miguel A. Gutiérrez-Naranjo, Pedro Real, Vanesa Sánchez-Canales
- 2010

In this paper we present a P systems-based solution for the Homology Groups of Binary 2D Image (HGB2I) Problem, a classical problem in Homology Theory. To this aim, we present a family of P systems which solves all the instances of the problem in the framework of Tissue-like P systems with catalysts. This new framework combines the membrane structure and… (More)

- Rocío González, Díaz, Pedro Real
- 2001

In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing chain level Steenrod squares [20, 21], in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [5]. As an application, we give here an algorithm for computing cup–i products over… (More)

- V Alvarez, J A Armario, Frau, P Real
- 2009

Let G be a group which admits the structure of an iterated semidirect product of finitely generated abelian groups. We provide a method for constructing a free resolution : X → Z Z of the integers over the group ring of G. The heart of this method consists of calculating an explicit contraction from the reduced bar construction of the group ring of G, B(Z… (More)

Membrane Computing is a new paradigms inspired from cellular communication. We use in this paper the computational devices called P systems to calculate in a general maximally parallel manner the homology groups of binary 2D images. So, the computational time to calculate this homology information only depends on the thickness of them.